An Exponential Deterministic--Randomized Gap in ERM-Oracle Complexity for Thresholds on an Unknown Order
Attias, Hanneke and Ramaswami (NeurIPS 2025) asked whether randomization provably reduces the oracle calls needed for online learning when the class is accessible only through an oracle. We study the instance they singled out: transductive online learning of thresholds on an unknown total order of T instances, with a consistency-type ERM oracle that returns a full concept consistent with a queried labeled set (or reports non-realizability). Our main result is a separation for a fixed natural oracle. When the oracle is the minimal-prefix rule (or the maximal-prefix rule), every deterministic learner makes M mistakes and Q calls with $M+Q\ge T-\varepsilon$ on some instance ($\varepsilon\in\...
| Authors | Xuan Li |
|---|---|
| Primary category | cs.LG |
| Published | 9 September 2026 |
| Last updated at source | 9 September 2026 |
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